Mathematics Commons^™

Rotary Honing: A Variant Of The Taylor Paint-Scraper Problem, Christopher Hills, H. Moffatt

Articles

The three-dimensional Row in a corner of fixed angle α induced by the rotation in its plane of one of the boundaries is considered. A local similarity solution valid in a neighbourhood of the centre of rotation is obtained and the streamlines are shown to be closed curves. The effects of inertia are considered and are shown to be significant in a small neighbourhood of the plane of symmetry of the flow. A simple experiment confirms that the streamlines are indeed nearly closed; their projections on planes normal to the line of intersection of the boundaries are precisely the 'Taylor' …

(Ω, Ξ)-Logic: On The Algebraic Extension Of Coalgebraic Specifications, Rolf Hennicker, Alexander Kurz

Engineering Faculty Articles and Research

We present an extension of standard coalgebraic specification techniques for statebased systems which allows us to integrate constants and n-ary operations in a smooth way and, moreover, leads to a simplification of the coalgebraic structure of the models of a specification. The framework of (Ω,Ξ)-logic can be considered as the result of a translation of concepts of observational logic (cf. [9]) into the coalgebraic world. As a particular outcome we obtain the notion of an (Ω, Ξ)- structure and a sound and complete proof system for (first-order) observational properties of specifications.

Maximally Disjoint Solutions Of The Set Covering Problem, David J. Rader, Peter L. Hammer

Mathematical Sciences Technical Reports (MSTR)

This paper is concerned with finding two solutions of a set covering problem that have a minimum number of variables in common. We show that this problem is NP­ complete, even in the case where we are only interested in completely disjoint solutions. We describe three heuristic methods based on the standard greedy algorithm for set covering problems. Two of these algorithms find the solutions sequentially, while the third finds them simultaneously. A local search method for reducing the overlap of the two given solutions is then described. This method involves the solution of a reduced set covering problem. Finally, …

Coupled Electrodynamic-Monte Carlo Simulations Of Nanoscale Gaas Terahertz Optical Mixers, Jiang Li

Electrical & Computer Engineering Theses & Dissertations

The concept of mixing or heterodyning has traditionally been used for microwaves and for radio frequency communications. However, the concept can easily be extended into the optical frequency regime. By doing so, the photomixing process can serve as a very versatile tool for both the generation of ultrahigh frequency (terahertz) and the detection of weak optical signals.

The aim of this thesis is to perform a theoretical study of the photomixing process inside GaAs devices as the non-linear elements. A coupled approach which combines the Monte Carlo simulation scheme for the carrier transport, with Maxwell's equation for the electrodynamics, has …

The Solution Of Hypersingular Integral Equations With Applications In Acoustics And Fracture Mechanics, Richard S. St. John

Mathematics & Statistics Theses & Dissertations

The numerical solution of two classes of hypersingular integral equations is addressed. Both classes are integral equations of the first kind, and are hypersingular due to a kernel containing a Hadamard singularity. The convergence of a Galerkin method and a collocation method is discussed and computationally efficient algorithms are developed for each class of hypersingular integral equation.

Interest in these classes of hypersingular integral equations is due to their occurrence in many physical applications. In particular, investigations into the scattering of acoustic waves by moving objects and the study of dynamic Griffith crack problems has necessitated a computationally efficient technique …

Representations, Approximations, And Algorithms For Mathematical Speech Processing, Laura R. Suzuki

Theses and Dissertations

Representing speech signals such that specific characteristics of speech are included is essential in many Air Force and DoD signal processing applications. A mathematical construct called a frame is presented which captures the important time-varying characteristic of speech. Roughly speaking, frames generalize the idea of an orthogonal basis in a Hilbert space, Specific spaces applicable to speech are L₂(R) and the Hardy spaces H_p(D) for p> 1 where D is the unit disk in the complex plane. Results are given for representations in the Hardy spaces involving Carleson's inequalities (and its extensions), …

Sparse Equation-Eigen Solvers For Symmetric/Unsymmetric Positive-Negative-Indefinite Matrices With Finite Element And Linear Programming Applications, Hakakizumwami Birali Runesha

Civil & Environmental Engineering Theses & Dissertations

Vectorized sparse solvers for direct solutions of positive-negative-indefinite symmetric systems of linear equations and eigen-equations are developed. Sparse storage schemes, re-ordering, symbolic factorization and numerical factorization algorithms are discussed. Loop unrolling techniques are also incorporated in the coding to enhance the vector speed. In the indefinite solver, which employs various pivoting strategies, a simple rotation matrix is introduced to simplify the computer implementation. Efficient usage of the incore memory is accomplished by the proposed "restart memory management" schemes. A sparse version of the Interior Point Method, IPM, has also been implemented that incorporates the developed indefinite sparse solver for linear …

Reverse Engineering Of Aircraft Wing Data Using A Partial Differential Equation Surface Model, Jacalyn M. Huband

Mathematics & Statistics Theses & Dissertations

Reverse engineering is a multi-step process used in industry to determine a production representation of an existing physical object. This representation is in the form of mathematical equations that are compatible with computer-aided design and computer-aided manufacturing (CAD/CAM) equipment. The four basic steps to the reverse engineering process are data acquisition, data separation, surface or curve fitting, and CAD/CAM production. The surface fitting step determines the design representation of the object, and thus is critical to the success or failure of the reverse engineering process. Although surface fitting methods described in the literature are used to model a variety of …

High-Order Finite-Difference Schemes And Their Application To Computational Acoustics, Joe Leo Manthey

Mathematics & Statistics Theses & Dissertations

The primary focus of this study is upon the numerical stability of high-order finite-difference schemes and their application to duct acoustics. Since acoustic waves are known to be non-dissipative and non-dispersive, high-order schemes are favored for their low dissipation and low dispersion relative to the low-order schemes. The primary obstacle to the the development of explicit high-order finite-difference schemes is the construction of boundary closures which simultaneously maintain the formal order of accuracy and the numerical stability of the overall scheme. In this thesis a hybrid seven-point, fourth-order stencil for computing spatial derivatives is presented and the time stability is …

Eigenvalue And Eigenvector Determination For Damped Gyroscopic Systems, D. P. Malone, Don L. Cronin, Timothy W. Randolph

Mechanical and Aerospace Engineering Faculty Research & Creative Works

No abstract provided.

Droplet Evaporation And Deformations In An Amplitude Modulated Ultrasonic Field, Nihad E. Daidzic, Rene Stadler, Adrian Melling

Aviation Department Publications

The aim of the report presented is the measurements of droplet oscillations.

Exact Solutions For Orthogonal And Non-Orthogonal Magnetohydrodynamic Stagnation-Point Flow, Shahrooz Moosavizadeh

Mathematics & Statistics Theses & Dissertations

The viscous plane flow of an electrically conducting fluid towards an infinite wall is solved in the presence of a magnetic field which is aligned with the flow far from the wall. The problem has two dimensionless parameters-- ε, the magnetic Prandtl number, and β, the square of the ratio of Alfven velocity to fluid velocity far from the wall. The problem has a similarity solution which reduces the governing equations to a system of coupled ordinary differential equations which can be solved numerically. For extreme values of ε, both large and small, singular perturbation techniques are used to derive …

Studies Of Mixing Processes In Gases And Effects On Combustion And Stability, Frank Paul Kozusko Jr.

Mathematics & Statistics Theses & Dissertations

Three physical models of laminar mixing of initially separated gases are studied. Two models study the effects of the mixing dynamics on the chemical reactions between the gases. The third model studies the structure and stability of a laminar mixing layer in a binary gas. The three models are:

1. Two ideal and incompressible gases representing fuel and oxidizer are initially at rest and separated across an infinite linear interface in a two dimensional system. Combustion, expected as the gases mix, will lead to a rapid rise in temperature in a localized area, i.e. ignition. The mixing of the gases …

Nozzle Flow With Vibrational Nonequilibrium, John Gary Landry

Mathematics & Statistics Theses & Dissertations

Flow of nitrogen gas through a converging-diverging nozzle is simulated. The flow is modeled using the Navier-Stokes equations that have been modified for vibrational nonequilibrium. The energy equation is replaced by two equations. One equation accounts for energy effects due to the translational and rotational degrees of freedom, and the other accounts for the affects due to the vibrational degree of freedom. The energy equations are coupled by a relaxation time which measures the time required for the vibrational energy component to equilibrate with the translational and rotational energy components. An improved relaxation time is used in this thesis. The …

A New Approach To Automatic Target Recognition Using Wavelet Transforms, Anitha Panapakkam, S. N. Balakrishnan, Daniel St. Clair

Computer Science Technical Reports

Automatic Target Recognition (ATR) systems have significant impact in defense applications. There is a continuing need to develop new and robust techniques to handle the increasingly complex ATR problem. The objectives of this thesis are two-fold. First a new technique to be used for ATR is developed and secondly an integrated ATR system to investigate and combine all subsystems is developed. In this thesis, we have developed a new technique for the feature extraction stage of ATR problem using wavelet transforms. Wavelet transforms have been one of the widely investigated areas of research in the past few years. The promising …

Gravity And Electromagnetism In Noncommutative Geometry, Giovanni Landi, Nguyen Ai Viet, Kameshwar C. Wali

Physics - All Scholarship

We present a unified description of gravity and electromagnetism in the framework of a Z 2 non-commutative differential calculus. It can be considered as a “discrete version” of Kaluza-Klein theory, where the fifth continuous dimension is replaced by two discrete points. We derive an action which coincides with the dimensionally reduced one of the ordinary Kaluza-Klein theory.

Multigrid Acceleration Of Time-Dependent Solutions Of Navier-Stokes Equations, Sarafa Oladele Ibraheem

Mechanical & Aerospace Engineering Theses & Dissertations

Recent progress in Computational Fluid Dynamics is encouraging scientists to look at fine details of flow physics of problems in which natural unsteady phenomena have hitherto been neglected. The acceleration methods that have proven very successful in steady state computations can be explored for time dependent computations. In this work, an efficient multigrid methods is developed to solve the time-dependent Euler and Navier-Stokes equations. The Beam-Warming ADI method is used as the base algorithm for time stepping calculations. Application of the developed algorithm proved very efficient in selected steady and unsteady test problems. For instance, the inherent unsteadiness present in …

Boundary Value Problems In Rectilinearly Anisotropic Thermoelastic Solids, Gilbert Kerr

Mathematics & Statistics Theses & Dissertations

The boundary value problems which are considered are the type that arise due to the presence of a Griffith crack (or cracks) in an anisotropic thermoelastic solid. The thermoelastic field, in such materials, when the infinitesimal theory is employed, is governed by a set of elliptic partial differential equations. The general solution of these equations is expressed in terms of arbitrary analytic functions whose real parts, in turn, are expressed in terms of Fourier type integrals or Fourier series. Integral transform techniques are then used to determine the stress intensity factors (and other pertinent information) for various crack geometries. In …

Electrostatic Positioning Of Droplets In Turbulent Flows (Lstm 375/Te/93), Nihad E. Daidzic, Adrian Melling

Aviation Department Publications

Report LSTM 375/TE/93, Lehrstuhl fuer Stroemungsmechanik Universitaet Erlangen-Nuernberg Cauerstr. 4, 8520 Erlangen Germany.

A Study Of The Interface Between A Turbulent Boundary Layer And The Irrotational Free Stream, Shih-Chao Lin

Mechanical & Aerospace Engineering Theses & Dissertations

A mathematical model has been developed to simulate the events which occur at the interface between a turbulent boundary layer and the irrotational free stream. By assuming the streamwise velocity component of this interface to be constant and that the interface is uncontorted initially, the solution to the equations of motion is used to derive the position functions of a point element on the interface. This analysis is restricted to a fully developed incompressible turbulent boundary layer with zero pressure gradient. Vertical velocity disturbances which are periodic in the spanwise direction and restricted to small streamwise domains are assumed.

The …

Frequency Domain Speech Compression Using The Karhunen-Loeve Transform, Donald W. Dryley

Theses and Dissertations

The purpose of this study was test the influence of phase on the quality of speech reproduced by a speaker dependent compression system. The tests consisted of compressing frequency domain speech vectors using the Karhunen-Loeve Transform, with and without phase, then making subjective judgements as to the reproduced quality. Error Metrics were then tested for their suitability as predictors of reproduced quality. The compression software transformed each speech vector into a vector of complex Fourier coefficients (only half of the coefficients are needed as transform is hermitian). Phase was preserved by using the real frequency components to form one vector …

Design And Implementation Of Fuzzy Logic Controllers, Osama A. Abihana

Electrical & Computer Engineering Theses & Dissertations

The main objectives of our research are to present a self-contained overview of fuzzy sets and fuzzy logic, develop a methodology for control system design using fuzzy logic controllers, and to design and implement a fuzzy logic controller for a real system. In this thesis we first present the fundamental concepts of fuzzy sets and fuzzy logic. Fuzzy sets and basic fuzzy operations are defined. In addition, for control systems, it is important to understand the concepts of linguistic variables, linguistic values, term sets, fuzzy rule base, inference methods, and defuzzification methods. Second, we introduce a four-step fuzzy logic control …

The Management Of Replicated Data, Hsueh-Chi Shih, C. Y. Ho, S. Alptekin

Computer Science Technical Reports

Data replication, which has the benefits of improving system availability and read performance, proved to be indispensable to many database applications. In a replicated database, the one-copy serializability of transaction executions can be ensured by employing a replica control mechanism on top of the traditional concurrency control mechanism. This work contains two replica control algorithms and a read-only transaction processing algorithm. Both replica control algorithms handle multiple site, communication and partitioning failures. The replica control algorithms achieve read operation efficiency by always translating a logical read operation into one local physical read operation and by taking advantage of the locality …

Bounds On Constraint Weight Parameters Of Hopfield Networks For Stability Of Optimization Problem Solutions, Gursel Serpen

Electrical & Computer Engineering Theses & Dissertations

The purpose of the presented research is to study the convergence characteristics of Hopfield network dynamics. The relation between constraint weight parameter values and the stability of solutions of constraint satisfaction and optimization problems mapped to Hopfield networks is investigated. A theoretical development relating constraint weight parameter values to solution stability is presented. The dependency of solution stability on constraint weight parameter values is shown employing an abstract optimization problem. A theorem defining bounds on the constraint weight parameter magnitudes for solution stability of constraint satisfaction and optimization problems is proved. Simulation analysis on a set of optimization and constraint …

The Solution Of A Singular Integral Equation Arising From A Lifting Surface Theory For Rotating Blades, Mark H. Dunn

Mathematics & Statistics Theses & Dissertations

A technique is presented for the solution of a linear, two dimensional, singular, Volterra integral equation of the first kind. The integral equation, originally developed by Farassat and Myers, is derived from the basic equations of linearized acoustics and models the lifting force experienced by an infinitesimally thin surface moving tangent to itself. As a particular application, the motion of modern high speed aircraft propellers (Advanced Technology Propellers) is considered. The unknown propeller blade surface pressure distribution is approximated by a piecewise constant function and the integral equation is solved numerically by the method of collocation. Certain simplifying assumptions applied …

On Shock Capturing For Liquid And Gas Media, Tze Jang Chen

Mathematics & Statistics Theses & Dissertations

The numerical investigation of shock phenomena in gas or liquid media where a specifying relation for internal energy is absent poses special problems. Classically, for gas dynamics the usual procedure is to employ a splitting scheme to remove the source terms from the Euler equations, then up-wind biased shock capturing algorithms are built around the Riemann problem for the system which remains. However, in the case where the Euler equations are formulated in the term of total enthalpy, a technical difficulty associated with equation splitting forces a pressure time derivative to be treated as a source term. This makes it …

Shadow Casting Phenomena At Newgrange, Frank Prendergast

Articles

A digital model of the Newgrange passage tomb and surrounding ring of monoliths known as the Great Circle is used to investigate sunrise shadow casting phenomena at the monument. Diurnal variation in shadow directions and lengths are analysed for their potential use in the Bronze Age to indicate the passage of seasonal time. Computer-aided simulations are developed from a photogrammetric survey to accurately show how three of the largest monoliths, located closest to the tomb entrance and archaeologically coded GC1, GC-1 and GC-2, cast their shadows onto the vertical face of the entrance kerbstone, coded K1. The phenomena occur at …

Linear Programming By G.V. Shenoy, New Delhi: Wiley Eastern Limited, 1989., A K Rao

IIMB Management Review

No abstract provided.

An Artificial Neural Approach To The Decomposition Problem, Chandrashekar L. Masti

Electrical & Computer Engineering Theses & Dissertations

The goal of this thesis is to develop an artificial neural approach toward addressing the intractability involved with the decomposition problem. The search for the lattice of substitution property (s. p.) partitions essential to decompositions is cast into the framework of constraint satisfaction. An artificial neural network is developed to provide solutions by performing optimization of a mathematically derived objective function over the problem space. The issue of transitivity is verified to belong to a class of problems beyond the scope of solvability for conventional quadratic-order constraint satisfaction neural networks. A theorem is stated and proved establishing that third-order correlations …

An Extension Of Essentially Non-Oscillatory Shock-Capturing Schemes To Multi-Dimensional Systems Of Conservation Laws, Jay Casper

Mathematics & Statistics Theses & Dissertations

In recent years, a class of numerical schemes for solving hyperbolic partial differential equations has been developed which generalizes the first-order method of Godunov to arbitrary order of accuracy. High-order accuracy is obtained, wherever the solution is smooth, by an essentially non-oscillatory (ENO) piecewise polynomial reconstruction procedure, which yields high-order pointwise information from the cell averages of the solution at a given point in time. When applied to piecewise smooth initial data, this reconstruction enables a flux computation that provides a time update of the solution which is of high-order accuracy, wherever the function is smooth, and avoids a Gibbs …